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"Add up the number of lemons in the 'ones box.' If there are ten or more lemons, put ten of the lemons in the 'tens box' and leave the extra lemons in the 'ones box.'"

For some children, boxes of lemons make it easier to learn addition with carrying. A new study indicates, however, that for most children the lemons - and trains, pizza slices and other examples frequently used to teach math - may just get in the way. Researchers from Ohio State University experimented with two different ways of teaching a new math concept: one method starting with abstract symbols, and one method starting with concrete examples involving tennis balls and measuring cups. Then they asked the two groups of students to apply what they had learned to a new situation, set up as a children's game. The students who had learned with abstract symbols were able to apply the new concept, while the other students performed no better than if they had been merely guessing.

"The motivation behind this research was to examine a very widespread belief about the teaching of mathematics," said researcher Jennifer A. Kaminski, "namely that teaching students multiple concrete examples will benefit learning. It was really just that, a belief." Kaminski explained that the tennis balls and measuring cups in the experiment did little for students' learning. "They tend to remember the superficial, the two trains passing in the night. It's really a problem of our attention getting pulled to superficial information."

The study may mean that math teachers should save real-world examples for later in the learning process, and then help students to apply the abstract concepts to such examples once they have mastered the math. Although the study tested college students, the researchers expect to see the same results with younger students. Early experiments with 11-year-olds seemed to confirm their hypothesis, and the team is now conducting more extensive research with elementary school students. (New York Times, 4-25-08)

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